Esakia order-compactifications and locally Esakia spaces
Logic
2025-12-29 v1 General Topology
Abstract
We introduce Esakia order-compactifications and study how they fit in the general theory of Priestley order-compactifications. We provide an analog of Dwinger's theorem by characterizing Esakia order-compactifications by means of special rings of upsets. These considerations naturally lead to the notion of a locally Esakia space, for which we prove that taking the largest Esakia order-compacification is functorial, thus obtaining an analog of Banaschewski's theorem.
Cite
@article{arxiv.2512.22042,
title = {Esakia order-compactifications and locally Esakia spaces},
author = {Rodrigo Nicolau Almeida and Guram Bezhanishvili and Nick Bezhanishvili},
journal= {arXiv preprint arXiv:2512.22042},
year = {2025}
}
Comments
19 pages, 3 figures